Well, every instance of Mirror Universe hinges on a cosmic coincidence - and a different one for each instance! But there's nothing wrong as such with a cosmic anomaly that hinges on a cosmic coincidence...

The "middle timeline" in this episode is not a unique one by any means. It's just one out of the infinite number that would have resulted in the E-C being sent back in time and giving birth to the regular TNG timeline. It's also a "lower rank" timeline, one that was predestined to only last for a few decades and culminate in its own nullification. Having it feature dramatically interesting characters is just a nice choice by the camera crew, which could have provided us with the view of just about any such timeline, including ones where completely unknown characters send the E-C back, and ones where the E-C is not sent back and everybody dies.